The solution to x^2-x-50<0 is (-sqrt(201)+1)/2 <x<(sqrt(201)+1)/2

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x^2-x-50<0

Solution

x^{2} - x - 50 < 0

\frac{- 201 + 1}{2} < x < \frac{201 + 1}{2}

Interval Notation

(\frac{- 201 + 1}{2}, \frac{201 + 1}{2})

Decimal Notation

- 6.58872 \dots < x < 7.58872 \dots

Solution steps

x^{2} - x - 50 < 0

Complete the square

x^{2} - x - 50 : (x - \frac{1}{2})^{2} - \frac{201}{4}

(x - \frac{1}{2})^{2} - \frac{201}{4} < 0

Move

\frac{201}{4}

to the right side

(x - \frac{1}{2})^{2} < \frac{201}{4}

For

u^{n} < a

, if

n

is even then

- \frac{201}{4} < x - \frac{1}{2} < \frac{201}{4}

a < u < b

then

a < u and u < b

- \frac{201}{4} < x - \frac{1}{2} and x - \frac{1}{2} < \frac{201}{4}

- \frac{201}{4} < x - \frac{1}{2} : x > \frac{- 201 + 1}{2}

x - \frac{1}{2} < \frac{201}{4} : x < \frac{201 + 1}{2}

Combine the intervals

x > \frac{- 201 + 1}{2} and x < \frac{201 + 1}{2}

Merge Overlapping Intervals

\frac{- 201 + 1}{2} < x < \frac{201 + 1}{2}

- \frac{3}{8} (x - 24) + x = 19

x (x + 8)^{2} (x - 5) < 0

7 y + 21

\frac{1}{3} - \frac{1}{4}

- x^{2} - 2 x - 5 = 0

What is x^2-x-50<0 ?
The solution to x^2-x-50<0 is (-sqrt(201)+1)/2 <x<(sqrt(201)+1)/2